Sunday, August 31, 2008

How old!?

I didn't post anything humorous for a lot of time, so here goes. As far as I know this one is a real story.
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Customer: “I’d like two tickets for [movie], please.”

Coworker: “That movie is rated R. Can I see your ID?”

Customer: *shows an ID that states she is 18*

Coworker: “You need to be 21 in order to purchase an R-rated ticket for someone else.”

Customer: “But it’s for my son!”

Coworker: “How old is your son?”

Customer: “16…”

Coworker: “So you’re 18… and you have a 16 year old son?”

Customer: “That’s right!”

Coworker: “Let me get my manager…”

Manager: “Ma’am, you need to be 21 to purchase a ticket for a minor.”

Customer: “But he’s my son!”

Manager: “You’re telling me you gave birth when you were two years old?”

Customer: “YES! It happens, I promise you!”

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I found this story here.

Wednesday, August 27, 2008

Overload

As you probably noticed, I didn't post for a few days. The reason for this is that I have to prepare to exams. Next week, the posting will continue as usual. Meanwhile, you are welcomed to use the skribit suggestion widget to suggest topics for me to write about.

Wednesday, August 20, 2008

Running in the rain

I was sent a letter yesterday which asked me to look and comment on the last claim on this page. Since that page might not remain forever, I am copying the paragraph in question:

You get less wet by running in the rain. Actual mathematical equations devoted to this popular question have suggested it is true, though not for the simple reasons you might think. Complexities include factoring in the number of rain drops hitting the walker’s head versus smacking the runner’s chest.

Well, lets do the calculations. While this sound like a complex problem it is actually a simple case of Galilean relativity, so it is easy to calculate.
The first step in dealing with a problem like this is to formulate it correctly. As I understand this problem, we need to prove or disprove the statement that if you stand still under the rain for some time T, you will be more wet than if you were running for the same time T.
The second step is to simplify the problem. In this case the simplification is to assume that the rain is uniform. That is, the amount of rain drops per square cm is the same in all the are we are dealing with, and there are no sudden changes in the wind.
Now, what we want to calculate is how wet will a person become. Clearly this depends on many factors - the size of the drops, the body area of the person, the speed of the rain drops etc. Because of the uniformity assumption we made, we can say that all the factors except for the speed of the rain are fixed - they don't change with time, and they don't change if the person is moving. We can now define the "wetness" (B) as a simple multiplication between the matrix A and a vector v. "A" will be the constant which we get from the problem condition. Since we are in 3d space A is a diagonal matrix with A1,A2,A3 (the corresponding constant for each one of the three directions) on the diagonal. "v" is the speed of the rain ( it is a vector v=(v1,v2,v3)). The multiplication result, B, is also a vector. The size of B multiplied by the time T is then the answer.

So if the person stands still under the rain we will get:

B=Av

T|B|=T

Now lets look what happens if a person starts to run. Since we can choose the coordinate system in any way we want we can assume the the person runs on the x axis with some speed w (for simplicity, we will assume that the speed is constant). Now it is time to use the Galilean transformation. From the coordinate system of the person the speed of the rain is no longer v=(v1,v2,v3). Instead it now becomes v'=(v1-w,v2,v3). Since nothing else changed, we will get:

B'=Av'

T|B'|=T

It is perfectly possible that this is less than the previous result, but it can also be large. It all depends on the direction of w. If for example w=v1, you will get less wet by running. But if w=-v1 you will get more wet if you will run.

This solution was done under the assumption that the rain is uniform. However, while this assumption is not realistic it is very close to reality and on a short time interval it should be extremely close to reality. It is possible to solve the problem without this assumption, but it will only introduce extra steps without changing the final result.

Monday, August 18, 2008

Fire and ice

I just stumbled on this image: ( click on the image to see the full size)

The reason I am posting it is that the image is in fact a fractal from the Mandelbrot set. It was edited pretty heavily, but the main part of the image is the classic Mandelbrot fractal.

By the way, if you are using Linux, there is an excellent program for generating fractals you can install. It also allows to add some effects to the resulting images generating impressive artwork. In Ubuntu you can install it by typing:
sudo aptitude install xaos

Sunday, August 17, 2008

The Department Quilt

Today I decided to do something I do very rarely - to look on the recommended feeds in Google Reader. I usually don't look on them, because I have almost 100 subscriptions already, and I don't want to add any extra feeds. However, today I decided to look on those feeds. In one of the feeds I suddenly saw a very familiar image:





These two images are the front and back sides of a quilt that can be found on the second floor of the mathematics department of Hebrew University Jerusalem. At first I thought that the blog author whose rss feed I was reading visited HUJI, and took those photos, but then I noticed that the post is called Our Department’s Quilt.

This is how because of a Quilt a found the blog of Gil Kalai - Combinatorics and more. He is a professor of mathematics in Huji. His main areas of interest are Combinatorics and convexity, so if you are interested in anyone of them, it is probably a good idea to visit his blog.

Saturday, August 16, 2008

Incredible military skills

Our present society is technology centered. It wasn't always like this, but it is so for a long time. However, better technology is not always the answer. As you can see in the movie below, it doesn't always help to point a gun to somebody head...

Friday, August 15, 2008

Wireless electricity

I was sent an interesting article yesterday about Atlantis. Most of this article is, as I call it, "conspiracy theories" - the most hilarious part is where the author claims that a mountain in Canada was shaped to resemble a head of an Indian. There is indeed such mountain, it was discovered by the users of Google earth. However, I really fail to see any reason to believe that this was done by humans and not by wind. I am so skeptical because if we assume that it was indeed build be someone, we get an even harder question: Why was it built? Constructions of this size are not built without a purpose, and I don't see any purpose to this one. It is not even art, since it can be viewed only from the air. The article in question also doesn't answer this.

Some of the claims in the article are clearly false (at least according to what I know), while some are true. In my opinion the only purpose of this article is to promote the theory it author has, and not to talk about facts. However it still makes an interesting read. Now to the main part of this post. One of the claims made in this article is that Atlantis used wireless electricity. This electricity was distributed from 13 towers (pillars) which were built in each of the 13 colonies. The author also refereed to Tesla, claiming that he started working on similar construction so this is perfectly possible. Moreover, Tesla was claiming that his device will provide everybody with free electricity from the earth ionosphere. But is this true? And if true, why don't we use this, relaying on wires instead?


Wireless power
Is it possible to power a device without wires? Of course it is. While working on his project Tesla build a room in which lamps (florescent) started to work even when not connected to the power outlets. This is based on the Faraday law - if we have a changing magnetic field we will get voltage. Tesla created a strong, constantly changing electromagnetic field in his room which powered his florescent lamp. There is no fiction in this, this principal is well known and is used on a daily basis - this is exactly how radio works. In a radio station, we have a transmitter that sends a changing electromagnetic wave in space, and this wave creates voltage on the radio antenna. in reality, this is slightly more complicated, but I don't want to get into the detailt of how a radio works.
Another way to transfer power without wires is to use displacement currents. This method was also known to Tesla, but it requires one wire so it is not exactly wireless.


Is it dangerous
From the above paragraph it is clear that if we want wireless power what we need is to create a strong electromagnetic field. Will such field have negative influence on people/other objects?
The answer to this is no and yes. People are not harmed by magnetic fields. The reason to this is that such fields influence only charges in motion or paramagnetic materials. Our bodies don't have any charge, and organic tissue is not paramagnetic. But, a computer in such a field would be fried immediately. The reason to this is that such field would not only supply power, it would effect all the circuits in the computer, and this would simply destroy them, probably with a little fire. It is possible to create a defense against such fields, there are materials which can block an electromagnetic field. But such a defense will have to be large and heavy.


Can it be done
So, we know that it is possible to transmit power without wires and we know how to protect computers and other gentle electronics from it. But can we use it? No. The reason for this is very simple. It is not a problem to create a strong magnetic field, but such fields become much less stronger with the distance. To be precise, the electromagnetic field drops as the square of the distance from the source. To bring some perspective, lets suppose that we have a field of 1000 Tesla. After what distance it will be only as strong as the field of the magnet you put on your refrigerator? The equation we get is:



And the solution is 100. This means that after 100 meters from the power source the field will be very small. But this is only a 1000 Tesla, right? So if we will take more it will be fine. Unfortunately, no. Tesla is a very large unit. It is simply impossible with current technologies to create magnetic fields so strong. The strongest steady magnet created until now is under 45 Tesla. Also, even if we will be capable of creating electromagnetic fields strong enough, such fields will also cause little pieces of iron to fly to the magnet like a bullet. Besides, think about all the power loses.
Because of the above mentioned problems, it is practically impossible to operate a city on such wireless power source. However, the method I discussed is only a simplified version of what Tesla wanted to build.

Was Tesla wrong?
Surprisingly, no. I am sure that all the points I mentioned above were known to him. However, he found a way to solve this problem. I am not going to describe his idea in detail, but basically the plan was to use the resonance frequency of the earth and the ionosphere as a conduction layer. Tesla even claimed that he was able to transmit power across 25 miles with only 5% power loss. So, theoretically it is indeed possible that a civilization that is described in the article existed and used such power source.
Now, after saying this it looks like an ideal moment to say what is the main problem I see with this article. This article is focused on the idea "how great was Atlantis". It even goes so far as to say that it was utopia to which our race will eventually return, by technological development. But even from the article itself it is clearly not true. And the reason for this is Faraday law. If you indeed use wireless electricity you don't "magically" transport it from one point to another. It still has to pass all the mid points. If there will be metal on its path, this metal according to Faraday law will act like a small generator - it will get small voltages an small currents ("small" is the best scenario). If you want to power a city in this way you need firstly to remove the metal from it. Which means to remove all technology, because as I explained above the electromagnetic field will not only power a circuit, but it will effect all of the parts of the circuit. For complex circuits this means that they will be simply fried (and this cannot be solved by technology advances). This sounds a bit paradoxical - if we cannot have technology in the city, then what good is wireless power? The answer is that such power would still allow two basic devices to work - lamps and motors. I don't know what you think about such life, but I clearly don't like it.
But if you will read the article, this is exactly how the cities are described. Cities build from stone - because they couldn't put metal inside the walls. Cities without writing, civilization without knowledge.

Bottom line
I do not believe that Atlantis existed. There are evidence that support the theory that at some point there was an advanced civilization on the earth. According to these evidence, there are reasons to believe that even space flight was within their reach. But this is not enough to conclude anything about what really happen. For example, from the information we now have it is perfectly possible to get to the conclusion that at some point the earth was visited by aliens, who "helped" humanity, and then after a war (either among themselves or with humans) left the earth. But all such theories go against the basic principal of science - the Occam razor.
Also, Atlantis has zero importance for us. If at some point in the future we will indeed meet aliens that will admit that they visited the earth and influenced our civilization, it would be an interesting historical fact but no more. This is why there is just no point or reason to search for it, whatever the search will bring no longer matters because we have a civilization of our own. There is no reason to try and think about new "conspiracy theories" about the past.